Abstract
Informally, a proof is an argument that convinces. Formally, a proof is of a formula, and is a finite object constructed according to fixed syntactic rules that refer only to the structure of formulas and not to their intended meaning. The syntactic rules that define proofs are said to specify a proof procedure. A proof procedure is sound for a particular logic if any formula that has a proof must be a valid formula of the logic. A proof procedure is complete for a logic if every valid formula has a proof. Then a sound and complete proof procedure allows us to produce “witnesses,” namely proofs, that formulas are valid.
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© 1998 Springer Science+Business Media Dordrecht
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Fitting, M., Mendelsohn, R.L. (1998). Tableau Proof Systems. In: First-Order Modal Logic. Synthese Library, vol 277. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5292-1_2
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DOI: https://doi.org/10.1007/978-94-011-5292-1_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5335-5
Online ISBN: 978-94-011-5292-1
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